Fitting with shared measurement uncertainty

Errors that affect several measurements together need a joint treatment. The new research objective uses the complete covariance matrix, preserving correlations between minutes, IMU axes and the GPS-dependent wind constraint. It holds that matrix fixed as model and nuisance coefficients change.

The calculation first rescales rows to avoid mixing numerical magnitudes from gyro rates and the wind constraint, then uses a Cholesky factor to whiten their joint residual. Existing parameter penalties are applied afterward. A singular or numerically unstable covariance produces an explicit failure; the calculation does not discard measurement directions or silently add artificial noise.

It reports the residual quadratic and Gaussian normalization separately. The normalization matters when covariance assumptions differ, even though it stays constant during a fit with one frozen matrix. These outputs do not select a correlation assumption, compare evidence across different wind models, or produce a calibrated Earth-model decision.

All six saved recordings were checked under all 36 persistence assumptions, giving 216 objective evaluations at their existing fitted parameters. No new optimum was fitted. The same 79 supported minutes remain throughout, and every scenario is preserved. Independent matrix solves and direct perturbations agree with the objective and its derivatives.

The check exposed an important distinction: measurement uncertainty does not describe all error in the wind approximation. The physical wind candidate already allows a 2 m/s discrepancy in its speed constraint. Using propagated GPS errors alone loses that allowance and gives excessive weight to the constraint.

A second frozen comparison therefore makes the existing allowance explicit: full shared-input measurement covariance plus an independent model-discrepancy component for the wind constraint. Shared GPS cross-correlations remain intact. The broad wind candidate has no such constraint and is unchanged. No allowance was tuned to the simulated truth or to achieve a model decision.

Across the three physical-wind cases, the measurement-only residual quadratic ranges from about 27,700 to 598,000. Retaining the registered discrepancy changes that range to about 167–336. Those are uncalibrated objective values at old fit states, not goodness-of-fit probabilities or evidence for an Earth model. The large change shows why a working likelihood must distinguish measurement error from limitations of its nuisance model.

The implementation separates local sampling covariance from penalized curvature. Neither is validated interval coverage. Covariances still come from provisional error assumptions linearized at saved free-fit states; they are not an outcome- independent design policy. Mounting, calibration, missing GPS correlations and instrument/systematic uncertainty remain open.

All 44 focused tests pass. Both sets of 216 objectives are independently checked; the broad-wind controls match their parent results. The first evaluation stage took about 54 summed seconds, and the discrepancy comparison about 7 seconds, using one numerical thread. Completed-scope resume checks skipped all cases. No new flights, optimizer calls, bootstrap, calibration or production changes ran.

The next proposed comparison uses the six saved recordings under four fixed GPS/IMU correlation pairs: independent/independent, 15s/15s, 300s/300s and 15s/300s. Each would receive a free fit and three fixed Earth-model fits: 96 fits, with at most one predefined nesting repair per case/assumption, or 120 starts total. This scope is proposed, not launched. It would retain the explicit discrepancy component, freeze each covariance across model comparisons, and report convergence, boundaries and raw objective differences without calibrated decisions. Runtime needs measurement; no new flights or bootstrap are proposed.

The documented corpus contains the first stage's plan.json, six task-named JSON/NPZ pairs, review.json, verification.json, status.json and run.lock. The wind-discrepancy/ subdirectory preserves the second stage in the same form. Both bind sources, inputs, parent artifacts and numerical environment. Completed artifacts and bound helpers are immutable. No worker remains active.